1. Field of the Invention
The present invention relates to a signal processing technique and, more particularly, to a blind signal separating method for separating respective signals from multi-channel multi-path mixed signals, and an apparatus for performing the same.
2. Description of the Related Art
In general, a plurality of signal sources in a multi-channel multi-path environment reach respective sensors via various paths and are mixed in the respective sensors. Among the various paths from the locations of the signal sources to the sensors, a direct path involves a time delay corresponding to relative locations of the signal sources and sensors.
An independent component analysis (ICA) technique, using the fact that signal sources are statically independent, estimates radio wave paths of signal sources from multi-channel signals and separates the signal sources, without any information regarding the signal sources provided in advance.
Also, a frequency domain ICA technique is a method in which an ICA is applied in each frequency. In this case, because the ICA is separately applied in each frequency, the separated signals are permutated, and one of the methods for solving such permutation phenomenon is utilizing direction information of the signals.
The method for separating a blind signal using the frequency domain ICA and the permutation phenomenon will now be described in detail. First, when an nth (n=1, . . . , N) signal source is sn(t) and an impulse response from the nth signal source to an mth (m=1, . . . , M) sensor is hmn, mixed signals (xm) collected from the mth sensor can be represented by Equation 1 shown below:
                              x          m                =                              ∑            n                    ⁢                                    h              mn                        *                          s              n                                                          [                  Equation          ⁢                                          ⁢          1                ]            
In Equation 1, * indicates convolution, and the impulse response hmn is a mixture filter administering the process of mixing the signal sources by the convolution. Signal processing is performed in a frequency domain, so mixed signals in a time domain are multiplied by a window function and then converted into signals of the frequency domain through short-time Fourier Transform.
The mixed signals in the frequency domain can be represented by Equation 2 shown below:
                                          x            m                    ⁡                      (                          f              ,              t                        )                          =                              ∑                          m              =              1                        M                    ⁢                                                    H                mn                            ⁡                              (                f                )                                      ⁢                          s              ⁡                              (                                  f                  ,                  t                                )                                                                        [                  Equation          ⁢                                          ⁢          2                ]            
In Equation 2, f indicates a frequency index, t indicates a time index, and xm(f,t), Hmn(f), sn(f,t) are those obtained as xm, hm, sn are Fourier-transformed, respectively. In general, the impulse response hmn changes over time, but hereinafter, it is assumed that the impulse response hmn is time-invariant for the sake of brevity.
When the signal sources and the mixed signals are defined as s(f,t)=[s1(f,t),sN(f,t)]T and x(f,t)=[x1(f,t),xn(f,t)]T in a vector form, the mixed signals can be represented by Equation 3 shown below:x(f,t)=H(f)s(f,t)  [Equation 3]
In the frequency domain, ICA with respect to a complex value (CICA: Complex-valued ICA) is separately applied in each frequency to calculate a separation filter W(f). An applicable CICA method includes FastICA (E. Bingham et al., “A fast fixed-point algorithm for independent component analysis of complex-valued signals,” International Journal of Neural Systems, vol. 10, no. 1, pp. 1-8, 2000) or InforMax (M. S. Pederson et al., “A survey of convolutive blind source separation methods,” in Multichannel Speech Processing Handbook, Jacob Benesty and Arden Huang, Eds, Springer, 2007), and the like.
The separated signals with respect to the mixed signals are calculated as represented by Equation 4 shown below:y(f,t)=W(f)x(f,t)  [Equation 4]
Because ICA is independently applied to each frequency and the statistical independence of signals is not related to the order of signals and change in amplitude of the signals, the resultantly calculated separation filters are sorted in random order in each frequency and have arbitrary sizes. These ambiguities will be referred to as permutation and scaling ambiguities. Here, the scaling ambiguity can be solved by a minimum distortion principle.
Also, various methods for solving the permutation problem of the frequency domain ICA have been proposed, and among the methods, a method of solving the permutation by using direction information of a separation filter is advantageous in that it can be employed irrespective of a type of signals and provides excellent performance.
When a far-field model, which disregards a signal echo and considers only a direct path because the distance between a sensor and a signal source are sufficiently long, is taken into account, the relationship between the direction of the signal and the mixture filter can be represented by Equation 5 shown below:
                                          H            mn                    ⁡                      (            f            )                          =                              λ            mn                    ⁢                      exp            ⁡                          (                                                j2π                  ⁢                                                                          ⁢                                      fd                    m                                    ⁢                                      sin                    ⁡                                          (                                              θ                        n                                            )                                                                      v                            )                                                          [                  Equation          ⁢                                          ⁢          5                ]            
In Equation 5, λm indicates an attenuation of a direct path, v indicates a radiowave speed of a signal, and dm and θn indicate the position of an mth sensor and a direction angle of an nth signal source based on the front side of the sensor when the position of a reference sensor m′ is set to be 0. The ratio of the direct path can be represented by Equation 6 shown below:
                              ∡          ⁡                      (                                                            h                  mn                                ⁡                                  (                  f                  )                                                                                                  h                                                                  m                        ′                                            ⁢                      n                                                        ⁡                                      (                    f                    )                                                  )                                      )                          =                                            2              ⁢              π              ⁢                                                          ⁢                              f                ⁡                                  (                                                                                    d                        m                                            ⁢                      sin                      ⁢                                                                                          ⁢                                              θ                        n                                                              v                                    )                                                      +                          2              ⁢              π              ⁢                                                          ⁢              k                                =                                    2              ⁢              π              ⁢                                                          ⁢              f              ⁢                                                          ⁢                              τ                mn                                      +                          2              ⁢              π              ⁢                                                          ⁢              k                                                          [                  Equation          ⁢                                          ⁢          6                ]            
In Equation 6, τmn indicates a relative delay time taken for the nth signal source to reach the mth sensor based on the reference sensor m′. The phase
  ∡  ⁡      (                            h          mn                ⁡                  (          f          )                                                  h                                          m                ′                            ⁢              n                                ⁡                      (            f            )                          )              )  has a value ranging from −π to π, so when the frequency is f≧1/(2|τmn|)≧ν/2dm, aliasing occurs, and at this time, the integer k has a value not 0.
As for respective streams of the separation filter W(f) obtained from the results of ICA, spectral nulls are positioned on a spatial spectrum in the direction of the signal sources in order to remove the remaining signals other than one signal. In this sense, the separation filter has information regarding the direction of the signal sources, which is mathematically equivalent to a null-beamformer.
Meanwhile, the separation filter is the converse of the mixture filter, so A(f)=W−1(f) obtained by taking the converse of the separation filter is equal to the size of the mixture filter H(f) except for the permutation. Thus, based on these characteristics, a method of estimating direction information of a signal source from A(f) and sorting the rows of A(f) such that they have the same direction information as the estimated direction information has been proposed. Here, as the scheme of sorting the rows of A(f), the converse of the separation filter, a k-means clustering scheme is applied. However, when spatial aliasing occurs due to a wide frequency band of a signal or due to a large space between sensors, because the k value has a value, not 0, a one-to-one corresponding relationship is not maintained between the direction information and phase information (or time delay information), so the method cannot be employed.
To offset the shortcomings, a method of setting a mixture filter as a direct path model having a time delay and attenuation factor and clustering the rows of A(f) by using the same has been proposed. A k-means clustering scheme is also applied to this method. However, as the k-means clustering scheme does not utilize statistical characteristics, its performance may be degraded in an environment in which an echo is large or background noise is present. In addition, in order to accurately normalize a phase, the approximate size of a sensor array must be known and information regarding the disposition of sensors, or the like, is required.
Another method for solving the permutation problem is a method of directly using the phase of a separation filter, rather than taking the converse of the separation filter. However, because this method utilizes W(f) forming a spectrum zero point with respect to a signal source, it cannot be applied to a case in which there are three or more signal sources. Also, this method does not consider statistical characteristics, the performance may be degraded in an area with excessive echo, and information regarding the size and disposition of a sensor array is required.